Analytical performance models are mathematical approximations of real world systems that can be used to predict certain behaviors of the systems being modeled. Examples of analytical modeling techniques can include, but are not limited to, Petri Net, colored Petri Net, and queuing theory. While each technique can be used to analyze different systems, queuing theory has been applied to a variety of modern systems. Queuing theory refers to the mathematical study of waiting lines, or queues. One type of system that can be modeled using queuing theory is a communication system that includes queuing servers. This is but one example as analytical models and queuing models can be used to model other real world systems such as bank or store check-out lines, telephone call banks, or the like.
With reference to a queuing model, once the model is created for a given system, the behavior of that system can be predicted in terms of different performance related measures. These measures can include, but are not limited to, the expected amount of time that a given object will be stored within a queue before being processed, the expected number of objects within a queue at a particular time, the probability the queue will be empty, the time to service for a particular type of object, or the like. Analytical models such as queuing models frequently are used to predict whether a particular system will be able to meet established quality of service metrics, such as response time.
Analytical models can use parameters measured from the actual system being modeled, which can be both difficult and costly to collect. In other cases, parameters from similar systems or parameters determined from past experience can be used. In any case, collecting too much information adds unnecessary cost to analytical model construction since the accuracy of the analytical model begins to converge to a fairly constant level despite increasing amounts of data. On the other hand, collecting too little information decreases cost but can result in an analytical model with a level of accuracy that is too low to be useful. Further complicating matters, once an analytical model has been built, the underlying, or modeled, system may undergo further change. This typically requires that the analytical model be rebuilt, which is a time consuming, manual process. It therefore becomes desirable to have some indication as to the amount of data needed to create an analytical model for a selected system.